In order to model turbulent flow, the following development from Seban and Faghri (1976) proceeds with assumptions similar to those made in the classical Nusselt laminar analysis. The momentum equation is

The solution requires choosing a turbulence model for the specification of and of The detailed turbulence model and solution procedure can be found in Seban and Faghri (1976). The predicted result agrees very well with the experimental result of Chun and Seban (1971) for constant heat flux at wall. To predict local heat transfer in turbulent falling film flow on a wall heated under constant heat flux, the following empirical correlation, recommended by Chun and Seban (1971), can be used:

As was demonstrated in Example 9.4, eq. (15) is valid for cases with either constant wall temperature or constant heat flux. However, the methods for determining the Reynolds number at x = L will vary for different thermal boundary conditions on the wall. For cases with constant wall temperature, the Reynolds number at x = L, , is obtained by substituting eq. (9.109) into eq. (15), i.e.,

While gravitational force drives the falling film evaporation discussed here, liquid flow in a liquid film can also be driven by centrifugal force. Rahman and Faghri (1992) analyzed the processes of heating and evaporation in a thin liquid film adjacent to a horizontal disk rotating about a vertical axis at a constant angular velocity. The fluid emanates axisymmetrically from a source at the center of the disk and then is carried downstream by inertial and centrifugal forces. Closed-form analytical solutions were derived for fully developed flow and heat transfer. Simplified analyses were also presented for developing heat transfer in a fully-developed flow field. Rice et al. (2005) provided a detailed analysis for evaporation from a thin liquid film on a rotating disk including conjugate effects.

Rahman, M.M., and Faghri, A., 1992, “Analysis of Heating and Evaporation from a Liquid Film Adjacent to a Horizontal Rotating Disk,” International Journal of Heat and Mass Transfer, Vol. 35, pp. 2644-2655.

Rice, J., Faghri, A., and Cetegen, B.M., 2005, “Analysis of a Free Surface Flow for a Controlled Liquid Impinging Jet over a Rotating Disk Including Conjugate Effects, with and without Evaporation,” International Journal of Heat and Mass Transfer, Vol. 48, pp. 5192-5204.